Collisions between two dissipative optical bullets separated in space

Abstract

We present the numerical results of both head-on and non-head-on collisions between two stable dissipative optical bullets (DOBs) in a three-dimensional complex Ginzburg-Landau equation with cubic-quintic nonlinearity. The system parameters chosen are in the coexistence regions for both stationary DOBs and double bullet complexes (DBCs). By varying the initial velocities v and the impact parameters P which represent the distance between the parallel trajectories of colliding bullets, we observe three generic properties of the bullets: fusion, fission, and quasi-elastic collisions. A novel and interesting behavior is observed in the results, in which two or three DBCs occur in non-head-on collisions at intermediate values of v. OCIS codes: 060.5530, 190.5530, 320.7110. doi: 10.3788/COL201109.100602. Recently, the concept of the dissipative soliton, which is rooted in the classical soliton theory, the nonlinear dynamics theory of bifurcations, and the concept of selforganization proposed by Prigogine, has received increased attention [1] . Dissipative solitons are recognized as fixed localized solutions resulting from a double balance: between dispersion and nonlinearity on one hand and between gain and loss on the other hand. Taking fiber laser as an example, the high-order vector soliton [2] and the dissipative dark soliton [3] occur as the balance between laser gain saturation and output loss, and the balance between cavity dispersion and the fiber nonlinear Kerr effect. Further, all dissipative solitons can only survive in the presence of a continuous energy supply. The cubic quintic complex Ginsburg-Landau equation (CGLE) is one of the notable models to describe dissipative solitons and is also applied to describe a variety of phenomena in optics. For example, CGLE appears in resonant atomic systems under electromagnetically induced transparency [4] and gain-assisted systems [5,6] . The dissipative optical system described by CGLE receives solitons in one-, two-, and three-dimensional (1D, 2D, and 3D) [7] . The formed solitons can propagate stably, provided that the system parameters are carefully chosen in the specified regions. 1D and 2D dissipative solitons have been studied extensively [4,8] , but the solitons in 3D systems have not. The spatial-temporal soliton in 3D dissipative optical systems, usually called dissipative optical bullet (DOB), is created by the combined interplay of physical effects such as gain and loss, spectral filtering and dispersion, and diffraction and nonlinearity. Similar to what atoms are combined together to form a diatomic molecule, DOBs can be bound into the bullet molecule as well. The bullet molecule, called double bullet complex (DBC), appears as a localized structure that can be stationary, pulsating, and rotating. Meanwhile, DOBs can coexist with DBCs in nonlinear dissipative systems, which form some parameter regions of coexistence. The bistability in these regions can be applied to switch to the desired state using an applied control beam [9] which offers a well-...